选择公理在数学分析演绎推理中的作用和意义

Role and Significance of Axiom of Choice in the Deductive Reasoning for Mathematical Analysis

每一个正确的数学演绎证明的逻辑结构,就是一个逻辑定理;反之每一个逻辑定理反映了一个正确的数学演绎推理规则。数学分析也不能例外,因各门学科都有自己的特点,所以运用这些逻辑定理的侧重点也不一样。因此,通过实例来探讨选择公理在数学分析演绎推理过程的重要作用的。

Each correct mathematical proof with the deductive logic structure is a logical theorem; Conversely every logical theorem reflects a correct mathematical deductive inference rule. Course of mathematical analysis is no exception, because each discipline has its own characteristics, the use of the focus for the logic theorem is not the same. This paper discusses the important role of axiom of choice in deductive reasoning process of the mathematical analysis through the example of the axiom of choice.